Atletico host Barcelona in the first leg on Feb. 1 with the second leg at the Nou Camp on Feb. 7.
Barcelona have won the Cup a record 28 times and have lifted it in the last two seasons under coach Luis Enrique, who said this week his ideal final would be against his former club Celta.
"They (Barca) are one of the best teams in the world so it's going to be a great tie and the games will be very tough. The tie will be decided by details, especially concentration, which we'll need if we're to go through," Atletico midfielder Koke said.
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Barca knocked Atletico out of the Cup at the quarter-final stage in 2015 4-2 on aggregate following an action-packed second leg in which Diego Simeone's side were reduced to nine men.
"It's vital we score at their place in the first leg. It's so evenly matched and we're going to have to put in two huge performances because Atletico always demand the maximum from you," Barca defender Sergi Roberto said.
Barca beat Real Sociedad 6-2 on aggregate to advance to the last four while Atletico saw off Eibar 5-2. Alaves beat Alcorcon 2-0 on aggregate and Celta knocked out La Liga leaders Real Madrid 4-3 on aggregate.
Celta have reached the final three times but never won the trophy.
They entertain Basque side Alaves, the 2001 UEFA Cup finalists who are bidding to reach their first King's Cup final, in the first leg on Feb. 2.
The final is on May 27 with the venue still to be determined, although Spanish media reported it will be at Atletico's Vicente Calderon, which is set to close at the end of the season.
(Editing by Ed Osmond)
